Climate Dilemma

After an international treaty is negotiated, it then has to be ratifed by its participants. This can be modelled as a two stage extensive form game. In Stage 1, the players negotiate the treaty; in Stage 2, each country decides whether to ratify the treaty. For some countries, for example the United States, ratification can be difficult. The United States requires 67 out of 100 Senate votes in order to ratify a treaty.

The most important solution concept for an extensive form game is known as a subgame perfect equilibrium. Each stage of the game is treated as a subgame. The subgame perfect equilibirum is an equilibirum which is also a Nash equilibirum for each subgame.

The main technique for calculating subgame perfect equilibria is known as backwards induction. In this technique the subgame perfect equilibria for the “last” subgames are calculated first. Then taking these actions as given, we calculate the equilibria for preceeding subgames and so on.

By backwards induction, for negotiators in Stage 1 to play the subgame perfect equilibrium, they will take into account that a treaty will have to be sufficiently aligned with the domestic interests of the United States, in order for it to be ratified by the United States.  The US Senate has two representatives from each state, so states with low populations (such as those in the midwest) are disproportionately represented. Coal is widely used in the midwest, and agriculture is an important industry. The US Senate is likely to want to see commitments from major developing countries. All of these issues are therefore likely to be important in international negotiations.

The US Senate will most probably consider the Waxman-Markey bill before the negotiations in Copenhagen commence. The Waxman-Markey bill will most likely require 60 out of 100 votes to avoid a filibuster. Issues that will affect the passage of the Waxman-Markey bill through the Senate will also be important for treaty ratification.